Question

The correct order in which the O-O bond length increases in the following is (a) \(\mathrm{O}_{2}<\mathrm{H}_{2} \mathrm{O}_{2}<\mathrm{O}_{3}\) (b) \(\mathrm{O}_{3}<\mathrm{H}_{2} \mathrm{O}_{2}<\mathrm{O}_{2}\) (c) \(\mathrm{H}_{2} \mathrm{O}_{2}<\mathrm{O}_{2}<\mathrm{O}_{3}\) (d) \(\mathrm{O}_{2}<\mathrm{O}_{3}<\mathrm{H}_{2} \mathrm{O}_{2}\)

Short answer

The correct order is (d) \(O_{2}<O_{3}<H_{2}O_{2}\).

Step-by-step solution

Analyzing the O-O bond in O2

In the molecule \(O_{2}\), there is a double bond between the oxygen atoms. Double bonds are shorter and stronger than single bonds. Therefore, the bond length in \(O_{2}\) is relatively short.

Understanding the O-O bond in H2O2

In \(H_{2}O_{2}\), also known as hydrogen peroxide, there is a single bond between the two oxygen atoms. Single bonds are longer than double bonds, so the O-O bond length in \(H_{2}O_{2}\) is longer than that of \(O_{2}\).

Analyzing the O-O bond in O3

In ozone \(O_{3}\), there is a resonance structure involving both single and double bond characteristics among the oxygen atoms. This results in an average bond length that is longer than a pure double bond but shorter than a pure single bond.

Arranging O-O bond lengths

Based on the bond types outlined, order the molecules by increasing bond length: \(O_{2}\) has the shortest bond length due to the double bond, \(O_{3}\) has a moderate bond length due to resonance, and \(H_{2}O_{2}\) has the longest bond length with a single bond. Thus, the correct order is \(O_{2}<O_{3}<H_{2}O_{2}\).

Key concepts

Double Bonds in Chemistry

Double bonds are a fundamental concept in chemistry, frequently encountered in molecules like oxygen gas (_2). When two oxygen atoms are bonded with a double bond, they share two pairs of electrons. This type of bond is characterized by shorter bond lengths and increased bond strength compared to a single bond.

• The sharing of two electron pairs leads to the formation of one sigma (σ) bond and one pi (π) bond.
• Due to the nature of the bonds, double bonds restrict the rotational movement between bonded atoms.
• Double bonds are generally more reactive than single bonds because the pi bond is less stable and can be easily broken or attacked in chemical reactions.

In the oxygen molecule (_2), this double bond results in a relatively short bond length. This is because the atoms are held more tightly together compared to the bond seen in _2O_2, where atoms only share one pair of electrons.

Resonance in Ozone

Ozone (_3) is a fascinating molecule that demonstrates the concept of resonance, which affects its bond characteristics. Resonance is a phenomenon where a molecule can be represented by two or more valid Lewis structures, known as resonance structures.
When it comes to ozone, its resonance involves alternating single and double bond representations between the oxygen atoms. This gives rise to average bonding characteristics:

• Both bond lengths in ozone are identical due to resonance, even though the resonance forms depict one single and one double bond.
• The actual bond length is an average, making it longer than a typical double bond, but shorter than a single bond.
• Resonance in ozone results in bond energy that is intermediate between the energies typically required to break single and double bonds.

Thus, ozone has a moderate bond length, influenced by the electron delocalization across the resonating structures.

Single Bond Characteristics

Single bonds, prevalent in many molecules like hydrogen peroxide (_2O_2), involve the sharing of one pair of electrons between two atoms. These are the simplest and longest type of covalent bonds, which can be seen in their characteristic traits:

• A single bond is composed solely of a sigma (σ) bond, which allows free rotation of bonded atoms.
• With longer bond lengths, single bonds generally exhibit lower bond energies than double or triple bonds, meaning they are weaker and easier to break.
• Single bonds are less reactive and more stable than double bonds, an advantage for molecules needing structural integrity.

In _2O_2, the presence of a single bond leads to a bond length that is longer than the averages seen in double-bonded or resonating molecules, further contributing to the unique reactivity and stability of hydrogen peroxide compared to purely single or double-bonded species.